The University of Newcastle, Australia
Available in 2019

Course handbook

Description

Complex analysis forms a basis for not only advanced mathematical topics (including differential equations, number theory, operator theory and others) but also for special functions of mathematical and quantum physics - subjects used to understand the world in which we live. The course covers fundamental knowledge in the theory of analytical functions with applications to definite integration and culminates with study of harmonic and special functions.


Availability2019 Course Timetables

Callaghan

  • Semester 2 - 2019

Learning outcomes

On successful completion of the course students will be able to:

1. Use analytical functions and conformal mappings;

2. Compute definite integrals using residue calculus;

3. Appreciate the existance of special functions and their use in a range of contexts.


Content

  • Functions of complex variable.
  • Differentiation of functions.
  • Cauchy's integral theorem.
  • The calculus of residues. Series expansions.
  • Contour integration.
  • Conformal mappings and further results on analytic functions.
  • Harmonic functions.
  • Entire functions and infinite products.
  • Special functions.

Assumed knowledge

MATH3242Complex AnalysisComplex analysis forms a basis for not only advanced mathematical topics (including differential equations, number theory, operator theory and others) but also for special functions of mathematical and quantum physics - subjects used to understand the world in which we live. The course covers fundamental knowledge in the theory of analytical functions with applications to definite integration and culminates with study of harmonic and special functions.FSCITFaculty of Science724School of Mathematical and Physical Sciences1030005980Semester 2 - 2019CALLAGHANCallaghan2019MATH2310 Functions of complex variable. Differentiation of functions. Cauchy's integral theorem. The calculus of residues. Series expansions. Contour integration. Conformal mappings and further results on analytic functions. Harmonic functions. Entire functions and infinite products. Special functions. YOn successful completion of this course, students will be able to:1Use analytical functions and conformal mappings;2Compute definite integrals using residue calculus;3Appreciate the existance of special functions and their use in a range of contexts. Written Assignment: Written AssignmentsQuiz: Quiz - ClassFormal Examination: Examination: Formal CallaghanLectureFace to Face On Campus3hour(s)per Week for0Full Term0Tutorial work will be integrated with the lecture material.


Assessment items

Written Assignment: Written Assignments

Quiz: Quiz - Class

Formal Examination: Examination: Formal


Contact hours

Callaghan

Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term

Tutorial work will be integrated with the lecture material.